// 最小路径和

package Leetcode;

class solution_064 {
    public int minPathSum(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        // dp[i][j]表示到达位置(i,j)的最小路径和
        int[][] dp = new int[m][n];
        // 初始化
        dp[0][0] = grid[0][0];
        for (int i = 1; i < m; i++)
            dp[i][0] = grid[i][0] + dp[i - 1][0];
        for (int j = 1; j < n; j++)
            dp[0][j] = grid[0][j] + dp[0][j - 1];
        // 状态转换方程：dp[i][j] = min(dp[i-1][j],dp[i][j-1]) + grid[i][j]
        for (int i = 1; i < m; i++)
            for (int j = 1; j < n; j++)
                dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
        return dp[m - 1][n - 1];
    }
}

public class Solution064 {

}